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aleksklad [387]
2 years ago
14

Give an example of two 2×2 matrices A and B, neither of which is the zero matrix or the identity matrix, such that AB=BA.

Mathematics
1 answer:
Katena32 [7]2 years ago
6 0

Let

A=B=\begin{bmatrix}0&1\\1&0\end{bmatrix}

Then

AB=BA=\begin{bmatrix}0&1\\1&0\end{bmatrix}^2=\begin{bmatrix}1&0\\0&1\end{bmatrix}

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If quadrilateral PQRS is a rectangle, then which of the following is true?
brilliants [131]

∠STP ≅ ∠QTR is the True statement ⇒ answer C

Step-by-step explanation:

In any rectangle

1. Each two opposite sides are equal and parallel

2. The measure of its vertex angles is 90°

3. The two diagonals are equal

Now lets find the true statements

∵ PQRS is a rectangle

∴ PS = QR ⇒ opposite sides

∴ PQ = SR ⇒ opposite sides

∴ PR = QS ⇒ diagonals

A.  ∠PSQ ≅ ∠QSR

∵ The diagonals of the rectangle do not bisect the vertex angles

∴ AQ does not bisect angle S

∴  m∠PSQ ≠ m∠QSR

∴  ∠PSQ not congruent ∠QSR

∠PSQ ≅ ∠QSR ⇒ False

B. segment SR ≅ segment RQ

∵ SR and RQ are two adjacent sides

∵ The adjacent side in the rectangle not equal

∴ SR ≠ QR

∴ segment SR not congruent to segment RQ

segment SR ≅ segment RQ ⇒ False

C. ∠STP ≅ ∠QTR

∵ PR intersects QS at point T

∴ m∠STP = m∠QTR ⇒ vertically opposite angles

∴ ∠STP ≅ ∠QTR

∠STP ≅ ∠QTR ⇒ True

D. segment PS ≅ segment PR

∵ PS is a side in the rectangle

∵ PR is a diagonal in the rectangle

∵ The side of the rectangle not equal the diagonal of the rectangle

∴ PS ≠ PR

∴ segment PS not congruent to segment PR

segment PS ≅ segment PR ⇒ False

∠STP ≅ ∠QTR is the True statement

Learn more:

You can learn more about rectangle in brainly.com/question/6594923

#LearnwithBrainly

8 0
2 years ago
Read 2 more answers
What is the sum of all positive integers smaller than $1000$ that can be written in the form $100\cdot 2^n$, where $n$ is an int
netineya [11]

Answer:

The sum is 1575.

Step-by-step explanation:

Consider the provided information.

It is given that positive integers smaller than 1000 and that can be written in the form 100\cdot 2^n

Where n is integer that means the value of n can be a positive number or a negative number.

For n = 0

100\cdot 2^{0}=100

For n=-1

100\cdot 2^{-1}=50

For n=-2

100\cdot 2^{-2}=25

For n = -3 the obtained number is not an integer.

Now consider the positive value of n.

For n=1

100\cdot2^1 = 200

For n=2

100\cdot2^2 = 400

 For n=3

100\cdot2^3 = 800

For n=4 the obtained number is greater than 1000.

Now add all the numbers.

100+50+25+200+400+800=1575

Hence, the sum is 1575.

6 0
2 years ago
An airliner carries 150 passengers and has doors with a height of 78 in. Heights of men are normally distributed with a mean of
iogann1982 [59]

Answer:

Step-by-step explanation:

x, height of men is N(69, 2.8)

Sample size n =150

Hence sample std dev = \frac{2.8}{\sqrt{150} } =0.229

Hence Z score = \frac{x-69}{0.229}

A) Prob that a random man from 150  can fit without bending

= P(X<78) = P(Z<3.214)=1.0000

B) n =75

Sample std dev = \frac{2.8}{\sqrt{75} } =0.3233

P(X bar <72) = P(Z<9.28) = 1.00

C) Prob of B is more relevent because average male passengers  would be more relevant than a single person

(D) The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

3 0
2 years ago
Circle groups to show 3x(2x3)
docker41 [41]
2x3=6x3=18 u always do PEMDAS,
5 0
2 years ago
Read 2 more answers
Two bicyclists are 7/8 of the way through a mile long tunnel when a train approaches the closer end at 40 mph. The riders take o
Anastaziya [24]

Answer:

the cyclists rode at 35 mph

Step-by-step explanation:

Assuming that the cyclists stopped, and accelerated instantaneously at the same speed than before but in opposite direction , then

distance= speed*time

since the cyclists and the train reaches the end of the tunnel at the same time and denoting L as the length of the tunnel :

time = distance covered by cyclists / speed of cyclists = distance covered by train / speed of the train

thus denoting v as the speed of the cyclists :

7/8*L / v = L / 40 mph

v = 7/8 * 40 mph = 35 mph

v= 35 mph

thus the cyclists rode at 35 mph

6 0
2 years ago
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